At the P. Nutty Peanut Company, dry roasted, shelled peanuts are placed in jars by a machine. The distribution of weights in the bottles is approximately Normal, with a mean of 16.1 ounces and a...

At the P. Nutty Peanut Company, dry roasted, shelled peanuts are placed in jars by a machine.  The distribution of weights in the bottles is approximately Normal, with a mean of 16.1 ounces and a standard deviation of 3.5 ounces.

a) What is the probability that the contents of a randomly selected jar will weigh between 15.9 ounces and 16.5 ounces?

b) Jars with weight less than k cm are rejected. Find the value of k if 4% of the jars are rejected. Leave your answer in two decimal places.

c) Suppose there are 30 samples of jars selected. Find the probability that the mean weight is more than 18 ounces. Leave your answer in four decimal places.